Mainstream points-to analysis techniques for object-oriented languages rely predominantly on the allocation-site abstraction to model heap objects. We present MAHJONG, a novel heap abstraction that is specifically developed to address the needs of an important class of type-dependent clients, such as call graph construction, devirtualization and may-fail casting. By merging equivalent automata representing type-consistent objects that are created by the allocation-site abstraction, MAHJONG enables an allocation-site-based points-to analysis to run significantly faster while achieving nearly the same precision for type-dependent clients. MAHJONG is simple conceptually, efficient, and drops easily on any allocation-site-based points-to analysis. We demonstrate its effectiveness by discussing some insights on why it is a better alternative of the allocation-site abstraction for type-dependent clients and evaluating it extensively on 12 large real-world Java programs with five context-sensitive points-to analyses and three widely used type-dependent clients. MAHJONG is expected to provide significant benefits for many program analyses where call graphs are required.